Combining strain and acceleration measurements for random force estimation via Kalman filtering on a cantilevered structure

Several engineering applications demand in-operation dynamic forces exerted on structural components to be modeled, however there are cases in which both phenomenological and empirical estimations are more uncertain than admissible. Although direct input measurements would be the first option to solve this lack, in many instances an appropriate and feasible instrumentation is hard to be accomplished due to reduced space, especial environment conditions (e.g. submerged structures), etc. leaving a gap for new methods to be explored. Virtual sensing represents a solution for determining forces when direct measurements are not feasible or present important technical challenges. In this context, augmented-state Kalman Filter (AKF) based techniques have recently been introduced in the field of force estimation. This technique consists in adding the unknown inputs (or input parameters) to the normal state vector of the mechanical system, which usually comprises only displacement and velocity states, and estimate the augmented-state vector in a Kalman Filter scheme. One of the challenges behind a successful AKF implementation is stability, as estimates based on acceleration tend to deviate with time. Dummy measurements have been used in the past as a means to guarantee stability. In this work, online dynamic strain measurements are used in that sense and the ability of the AKF for estimating a point force random in time, is successfully evaluated. In order to validate this procedure, the present experimental approach features a cantilevered structure, instrumented with standard accelerometers and dynamic strain sensors, excited with a known force. A force sensor is used to directly measure the input force for further comparisons, which show good agreement both in time and frequency domain.